11 questions linked to/from Difficulties with bra-ket notation
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I saw it in this pdf, where they state that $P=P^\dagger$ and thus $P$ is hermitian. I find this notation confusing, because an operator A is Hermitian if $\langle \Psi | A \Psi \rangle=\langle A \... 2answers 3k views ### Existence of adjoint of an antilinear operator, time reversal The time reversal operator$T$is an antiunitary operator, and I saw$T^\dagger$in many places (for example when some guy is doing a "time reversal"$THT^\dagger$), but I wonder if there is a well-... 3answers 1k views ### Dirac notation - specific acting orientation for operators I have this doubt: Imagine two operators$A$and$B$and the state$\psi$. I know that the following statement is true: $$\langle\psi| A|\psi\rangle^*=\langle\psi| A^\dagger|\psi\rangle$$ But is ... 2answers 1k views ### Adjoint of a Wave Function Why is the adjoint of a function simply it's complex conjugate? Normally with a vector we consider the adjoint to be the transpose (And the conjugate? I don't know why), so does this concept carry ... 3answers 591 views ### How do you show that momentum is hermitian in Dirac notation? I am trying to prove that momentum operator$\bf{\hat{p}}$is hermitian. I know how to prove it in the$\bf{x}$representation integrating by parts and using the fact that$\lim_{r \rightarrow \infty} ...
I want to prove the following identity: $$\langle v|\Omega^{\dagger}|u\rangle = \langle u|\Omega | v \rangle^*$$ How should I go about this? I believe I can prove it when $\Omega$ is hermitian, but ...